The learning curve The learning curve

Abstract (98 words) Most tasks get faster with practice. This holds across task size and task type. Learning curves plot time to complete a task as a function of practice. Such curves generally follow what is called a power law, thus, they are often said to conform to "the power law of practice". Cognitive psychology has shown that the power law of practice is ubiquitous, and cognitive modeling has explained both the general speedup and variability in performance, which previously was taken to be noise. Research is ongoing to find out why it is ubiquitous and where it does not apply. Ritter and Schooler Powerlaw of learning for IES&BS 3 November 22, 2002 The learning curve Most tasks get faster with practice. This is not surprising because we have all seen this and perhaps know it in some intuitive sense. What is surprising is that the rate and shape of improvement is fairly common across tasks. There are some related regularities. There is evidence to suggest that standard deviation and skew in performance time also decrease according to a power law, but with worse correlations. Indeed, in some cases the decrease in standard deviations appears to cause the improvement, because the minimum time to perform a task does not change The power law of practice is ubiquitous. From short perceptual tasks to team-based longer term tasks of building ships, the breadth and length of human behavior, the rate that people improve with practice appears to follow a similar pattern. It has been seen in pressing buttons, reading inverted text, rolling cigars, generating geometry proofs and manufacturing machine tools (cited in Newell and Rosenbloom, 1981), performing mental arithmetic on both large and small tasks Ritter and Schooler Powerlaw of learning for IES&BS 4 November 22, 2002 long it takes to complete over 10 trials, or better over a hundred trials. For example, try reading this article upside down. The time per paragraph will generally decrease, but with some differences caused by the different words and paragraph lengths. In general, the more averaging, the smoother the curve. The learning curve appears smoother when the data is averaged across subjects, across tasks, or both. When the tasks are known to vary in difficulty, such as different complex mental arithmetic problems (e.g., 27x5 and 23x28), the learning curve only appears when averaging is performed because the different problems naturally take different times. Even when problems are of comparable difficulty, subjects may use different strategies. For example, arithmetic problems can be solved by two strategies, retrieval and calculation. The power law applies across strategies, but the fit is better to each strategy (Delaney et al., 1998), or even an individual's strategies (Heathcote et al, in press). Averaging can mask important aspects of learning. If the tasks vary in difficulty, the resulting line will not appear as a smooth curve, but bounce around. Careful analysis can show that different amounts of transfer and learning are occurring on each task. For example, solving the problem 22x43 will be helped more by previously solving 22x44 than by solving 17x38 because there are more multiplications shared between them. Where sub-tasks are related but different, such as sending and receiving Morse code, the curves can be related but visibly different (Bryan & Harter, 1897). The learning curve has implications for learning in education and everyday life. It suggests that practice always helps improve performance, but that the most dramatic improvements happen first. Another implication is that with sufficient practice people can achieve comparable levels of performance. For example, extensive practice on mental arithmetic (Staszewski reported in Delaney et al., 1998) and on digit memorization have turned average individuals into world class performers. To sum up, the learning curve is visible with enough aggregation of dissimilar tasks or across similar tasks down to the level of individual subject's strategies. Ritter and Schooler Powerlaw of learning for IES&BS 5 November 22, 2002 Mathematical definitions The shape of the curve is negatively accelerated --further practice improves performance, but with diminishing returns. Power laws and exponentials are both functions that provide this shape. Mathematical definitions are given in In general, the power function fit appears to be robust, regardless of the methods used Ritter and Schooler Powerlaw of learning for IES&BS 6 November 22, 2002 Process based explanations of the learning curve The power law of learning is an important regularity of human behavior that all theories of learning must address. For example, Logan (1988) suggests that the retrieval of memory traces guides responding in speeded tasks. Response times represent the fastest retrieval time among the memory traces racing to guide the response. The power law falls out of this analysis, because with practice the number of redundant memory traces increases, which, in turn, increases the chances of observing fast retrieval times. Olhsson's (1996) theory notes how the learning curve could arise out of error correction. Different assumptions (e.g., how fast errors are caught) give rise to different curves including the exponential and power law. The learning curve has also been demonstrated for connectionist models as well. ACT-R (J. R. Ritter and Schooler Powerlaw of learning for IES&BS 7 November 22, 2002 a period. Soar and ACT-R also predict variance in the improvement on all tasks due to different amounts of transfer across problems and learning episodes. Summary The learning curve is a success story for cognitive psychology, which has shown that learning is ubiquitou